MinT - Best Known (70, 70+31, s)-Nets in Base 3

Best Known (70, 70+31, s)-Nets in Base 3

(70, 70+31, 148)-Net over F₃ — Constructive and digital

Digital (70, 101, 148)-net over F₃, using

5 times m-reduction [i] based on digital (70, 106, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 53, 74)-net over F₉, using
  - net from sequence [i] based on digital (17, 73)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
      - a function field by GarcÃa and Quoos [i]

(70, 70+31, 236)-Net over F₃ — Digital

Digital (70, 101, 236)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(70, 70+31, 4855)-Net in Base 3 — Upper bound on s

There is no (70, 101, 4856)-net in base 3, because

1 times m-reduction [i] would yield (70, 100, 4856)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 515857 071177 894655 814626 968096 826795 226189 159841 > 3¹⁰⁰ [i]